Object fabricated from a workpiece machined using a computer controlled machine tool along an asymmetric spiral tool path

ABSTRACT

An automated computer-implemented method for generating commands for controlling a computer numerically controlled machine to fabricate an object from a workpiece, the method including the steps of selecting a maximum permitted engagement angle between a rotating cutting tool and the workpiece, selecting a minimum permitted engagement angle between the rotating cutting tool and the workpiece, and configuring a tool path for the tool relative to the workpiece in which the engagement angle gradually varies between the maximum permitted engagement angle and the minimum permitted engagement angle.

REFERENCE TO RELATED APPLICATIONS

The present application is a continuation application of U.S. patentapplication Ser. No. 14/700,881, filed Apr. 30, 2015, entitledCOMPUTERIZED TOOL PATH GENERATION, now U.S. Pat. No. 9,823,645, which isa continuation application of U.S. patent application Ser. No.13/916,918, filed Jun. 13, 2013, entitled COMPUTERIZED TOOL PATHGENERATION, now U.S. Pat. No. 9,052,704, which is a divisionalapplication of U.S. patent application Ser. No. 13/036,726, filed Feb.28, 2011, entitled COMPUTERIZED TOOL PATH GENERATION, now U.S. Pat. No.8,489,224, the disclosures of which are hereby incorporated byreference.

FIELD OF THE INVENTION

The present invention relates to systems and methodologies for automatedtool path design and computer controlled machining and products producedthereby.

BACKGROUND OF THE INVENTION

The following publications are believed to represent the current stateof the art and are hereby incorporated by reference:

U.S. Pat. Nos. 4,745,558; 4,907,164; 5,363,308; 6,363,298; 6,447,223;6,591,158; 7,451,013; 7,577,490 and 7,831,332; and

US Published Patent Application No. 2005/0256604.

SUMMARY OF THE INVENTION

The present invention seeks to provide systems and methodologies forautomated tool path design and computer controlled machining andproducts produced thereby.

There is thus provided in accordance with a preferred embodiment of thepresent invention an automated computer-implemented method forgenerating commands for controlling a computer numerically controlledmachine to fabricate an object from a workpiece, the method includingthe steps of selecting a maximum permitted engagement angle between arotating cutting tool and the workpiece, selecting a minimum permittedengagement angle between the rotating cutting tool and the workpiece,and configuring a tool path for the tool relative to the workpiece inwhich the engagement angle gradually varies between the maximumpermitted engagement angle and the minimum permitted engagement angle.

In accordance with a preferred embodiment of the present invention,responsive to consideration of at least one of characteristics of thecomputer numerically controlled machine, rotating cutting tool andmaterial of the workpiece, the configuring also includes minimizing,subject to other constraints, the rate of change of the engagement angleover time, gradually changing the feed speed of the tool correspondingto the changing engagement angle, maintaining a generally constant workload on the tool, and minimizing the cost of fabricating the object,whereby the cost is a combination of the cost of operating the machinefor the duration of the fabrication and the cost of the wear inflictedon the tool during the fabrication.

Preferably, the tool path includes a plurality of tool path segments andconfiguring a tool path includes recursively configuring each of thetool path segments, and wherein responsive to consideration of at leastone of characteristics of the computer numerically controlled machine,rotating cutting tool and material of the workpiece, configuring each ofthe tool path segments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsegments, whereby the cost is a combination of the cost of operating themachine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

Additionally, each of the tool path segments includes a plurality oftool path subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

There is also provided in accordance with another preferred embodimentof the present invention a method for machining a workpiece employing acomputer controlled machine tool, the method including directing thetool along a tool path wherein an engagement angle between the tool andthe workpiece gradually varies between a preselected maximum permittedengagement angle and a preselected minimum permitted engagement angle.

There is further provided in accordance with yet another preferredembodiment of the present invention an automated computer-implementedapparatus for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece, theapparatus including a tool path configuration engine operative forconfiguring a tool path for a tool relative to the workpiece in whichthe engagement angle gradually varies between a preselected maximumpermitted engagement angle and a preselected minimum permittedengagement angle.

Preferably, the configuring includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time.Preferably, the configuring also includes gradually changing the feedspeed of the tool corresponding to the changing engagement angle.Preferably, the configuring is also operative to maintain a generallyconstant work load on the tool. Preferably, the configuring is alsooperative to minimize the cost of fabricating the object, whereby thecost is a combination of the cost of operating the machine for theduration of the fabrication and the cost of the wear inflicted on thetool during the fabrication. The preferred features referenced in thisparagraph are also applicable to all appropriate claimed embodiments ofthe present invention.

Preferably, the tool path includes a plurality of tool path segments andconfiguring a tool path includes recursively configuring each of thetool path segments, and wherein the configuring each of the tool pathsegments also includes minimizing, subject to other constraints, therate of change of the engagement angle over time, gradually changing thefeed speed of the tool corresponding to the changing engagement angle,maintaining a generally constant work load on the tool, and minimizingthe cost of machining the each of the tool path segments, whereby thecost is a combination of the cost of operating the machine for theduration of the machining and the cost of the wear inflicted on the toolduring the machining. The preferred features referenced in thisparagraph are also applicable to all appropriate claimed embodiments ofthe present invention.

Preferably, each of the tool path segments includes a plurality of toolpath subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein the configuring each of the tool pathsubsegments also includes minimizing, subject to other constraints, therate of change of the engagement angle over time, gradually changing thefeed speed of the tool corresponding to the changing engagement angle,maintaining a generally constant work load on the tool, and minimizingthe cost of machining the each of the tool path subsegments, whereby thecost is a combination of the cost of operating the machine for theduration of the machining and the cost of the wear inflicted on the toolduring the machining. The preferred features referenced in thisparagraph are also applicable to all appropriate claimed embodiments ofthe present invention.

Preferably, the configuring also includes considering at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece. The preferred featuresreferenced in this paragraph are also applicable to all appropriateclaimed embodiments of the present invention.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-controlledmachine to fabricate an object from a workpiece, the machine including acontroller operative for directing a rotating cutting tool along a toolpath relative to the workpiece in which an engagement angle between thetool and the workpiece gradually varies between a preselected maximumpermitted engagement angle and a preselected minimum permittedengagement angle.

There is yet further provided in accordance with still another preferredembodiment of the present invention an object fabricated from aworkpiece machined using a computer controlled machine tool by directinga rotating cutting tool along a tool path wherein an engagement anglebetween the rotating cutting tool and the workpiece gradually variesbetween a preselected maximum permitted engagement angle and apreselected minimum permitted engagement angle.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-implementedmethod for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece, the methodincluding the steps of selecting a region of the workpiece to be removedby a rotating cutting tool, configuring an asymmetric spiral tool pathfor the rotating cutting tool in the region of the workpiece, whichasymmetric spiral tool path maximizes the portion of the region of theworkpiece which is removed by the rotating cutting tool moving along theasymmetric spiral tool path.

Preferably, the method also includes configuring at least onetrochoidal-like tool path for the rotating cutting tool in a remainingportion of the region of the workpiece which is removed by the toolmoving along the trochoidal-like tool path.

Preferably, the method also includes selecting a maximum permittedengagement angle between a rotating cutting tool and the workpiece,selecting a minimum permitted engagement angle between the rotatingcutting tool and the workpiece, and configuring the asymmetric spiraltool path and the at least one trochoidal-like tool path relative to theworkpiece so that the engagement angle gradually varies between themaximum permitted engagement angle and the minimum permitted engagementangle.

Preferably, responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost offabricating the object, whereby the cost is a combination of the cost ofoperating the machine for the duration of the fabrication and the costof the wear inflicted on the tool during the fabrication.

Preferably, the asymmetric spiral tool path includes a plurality ofspiral tool path segments, the at least one trochoidal-like tool pathincludes a plurality of trochoidal-like tool path segments, configuringan asymmetric spiral tool path includes recursively configuring each ofthe spiral tool path segments, and configuring at least onetrochoidal-like tool path includes recursively configuring each of thetrochoidal-like tool path segments, and wherein responsive toconsideration of at least one of characteristics of the computernumerically controlled machine, rotating cutting tool and material ofthe workpiece, the configuring each of the tool path segments alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost ofmachining the each of the tool path segments, whereby the cost is acombination of the cost of operating the machine for the duration of themachining and the cost of the wear inflicted on the tool during themachining.

Additionally, each of the tool path segments includes a plurality oftool path subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

Preferably, the asymmetric spiral tool path is one of a convergingspiral tool path and a diverging spiral tool path.

There is yet further provided in accordance with still another preferredembodiment of the present invention a method for machining a workpieceemploying a computer controlled machine tool, the method includingselecting a region of the workpiece to be removed by a rotating cuttingtool, and directing the tool along an asymmetric spiral tool path in theregion of the workpiece, wherein the asymmetric spiral tool pathmaximizes the portion of the region of the workpiece which is removed bythe rotating cutting tool moving along the asymmetric spiral tool path.Preferably, the method also includes directing the rotating cutting toolalong at least one trochoidal-like tool path in a remaining portion ofthe region of the workpiece which is removed by the tool moving alongthe trochoidal-like tool path.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-implementedapparatus for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece, theapparatus including a tool path configuration engine operative forselecting a region of the workpiece to be removed by a rotating cuttingtool, and for configuring an asymmetric spiral tool path for therotating cutting tool in the region of the workpiece, which spiral toolpath maximizes the portion of the region of the workpiece which isremoved by the rotating cutting tool moving along the asymmetric spiraltool path.

Preferably, the tool path configuration engine is also operative forconfiguring at least one trochoidal-like tool path for the rotatingcutting tool in a remaining portion of the region of the workpiece whichis removed by the tool moving along the trochoidal-like tool path.

Preferably, the configuring includes selecting a maximum permittedengagement angle between a rotating cutting tool and the workpiece,selecting a minimum permitted engagement angle between the rotatingcutting tool and the workpiece, and configuring the asymmetric spiraltool path and the at least one trochoidal-like tool path relative to theworkpiece so that the engagement angle gradually varies between themaximum permitted engagement angle and the minimum permitted engagementangle.

Preferably, the configuring includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time.Preferably, the configuring also includes gradually changing the feedspeed of the tool corresponding to the changing engagement angle.Preferably, the configuring is also operative to maintain a generallyconstant work load on the tool. Preferably, the configuring is alsooperative to minimize the cost of fabricating the object, whereby thecost is a combination of the cost of operating the machine for theduration of the fabrication and the cost of the wear inflicted on thetool during the fabrication.

Preferably, the asymmetric spiral tool path includes a plurality ofspiral tool path segments, the at least one trochoidal-like tool pathincludes a plurality of trochoidal-like tool path segments, configuringan asymmetric spiral tool path includes recursively configuring each ofthe spiral tool path segments, and configuring at least onetrochoidal-like tool path includes recursively configuring each of thetrochoidal-like tool path segments, and wherein responsive toconsideration of at least one of characteristics of the computernumerically controlled machine, rotating cutting tool and material ofthe workpiece, the configuring each of the tool path segments alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost ofmachining the each of the tool path segments, whereby the cost is acombination of the cost of operating the machine for the duration of themachining and the cost of the wear inflicted on the tool during themachining.

Additionally, each of the tool path segments includes a plurality oftool path subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

Preferably, the asymmetric spiral tool path is one of a convergingspiral tool path and a diverging spiral tool path.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-controlledmachine to fabricate an object from a workpiece, the machine including acontroller operative for selecting a region of the workpiece to beremoved by a rotating cutting tool, and for directing the rotatingcutting tool along an asymmetric spiral tool path in the region of theworkpiece, which spiral tool path maximizes the portion of the region ofthe workpiece which is removed by the rotating cutting tool moving alongthe asymmetric spiral tool path.

Preferably, the controller is also operative for directing the rotatingcutting tool along at least one trochoidal-like tool path in a remainingportion of the region of the workpiece which is removed by the toolmoving along the trochoidal-like tool path.

There is yet further provided in accordance with still another preferredembodiment of the present invention an object fabricated from aworkpiece machined using a computer controlled machine tool by selectinga region of the workpiece to be removed by a rotating cutting tool andby directing the rotating cutting tool along an asymmetric spiral toolpath in the region of the workpiece, which spiral tool path maximizesthe portion of the region of the workpiece which is removed by therotating cutting tool moving along the asymmetric spiral tool path.

Preferably, the object is fabricated also by directing the rotatingcutting tool along at least one trochoidal-like tool path in a remainingportion of the region of the workpiece which is removed by the toolmoving along the trochoidal-like tool path.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-implementedmethod for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece, the methodincluding the steps of selecting a region of the workpiece to be removedby a rotating cutting tool, selecting a first portion of the region tobe removed by an asymmetric spiral tool path, and configuring at leastone trochoidal-like tool path for removing a remaining portion of theregion, and wherein the selecting a first portion of the region isoperative to minimize the machining time necessary to remove the region.

Preferably, the method also includes selecting a maximum permittedengagement angle between a tool and the workpiece, selecting a minimumpermitted engagement angle between the tool and the workpiece, andconfiguring the asymmetric spiral tool path and the at least onetrochoidal-like tool path relative to the workpiece so that theengagement angle gradually varies between the maximum permittedengagement angle and the minimum permitted engagement angle.

Preferably, responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost offabricating the object, whereby the cost is a combination of the cost ofoperating the machine for the duration of the fabrication and the costof the wear inflicted on the tool during the fabrication.

Preferably, the asymmetric spiral tool path includes a plurality ofspiral tool path segments, the at least one trochoidal-like tool pathincludes a plurality of trochoidal-like tool path segments, theconfiguring an asymmetric spiral tool path includes recursivelyconfiguring each of the spiral tool path segments, the configuring atleast one trochoidal-like tool path includes recursively configuringeach of the trochoidal-like tool path segments, and wherein responsiveto consideration of at least one of characteristics of the computernumerically controlled machine, rotating cutting tool and material ofthe workpiece, the configuring each of the tool path segments alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost ofmachining the each of the tool path segments, whereby the cost is acombination of the cost of operating the machine for the duration of themachining and the cost of the wear inflicted on the tool during themachining.

Preferably, each of the tool path segments includes a plurality of toolpath subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

Preferably, the asymmetric spiral tool path is one of a convergingspiral tool path and a diverging spiral tool path.

There is yet further provided in accordance with still another preferredembodiment of the present invention a method for machining a workpieceemploying a computer controlled machine tool, the method includingselecting a region of the workpiece to be removed by a rotating cuttingtool, selecting a first portion of the region to be removed by anasymmetric spiral tool path, and directing the tool along at least onetrochoidal-like tool path in a remaining portion of the region of theworkpiece, and wherein selecting a first portion of the region isoperative to minimize the machining time necessary to remove the region.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-implementedapparatus for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece, theapparatus including a tool path configuration engine operative forselecting a region of the workpiece to be removed by a rotating cuttingtool, selecting a first portion of the region to be removed by anasymmetric spiral tool path and for configuring at least onetrochoidal-like tool path for removing a remaining portion of theregion, and wherein the selecting a first portion of the region isoperative to minimize the machining time necessary to remove the region.

Preferably, the configuring includes selecting a maximum permittedengagement angle between a rotating cutting tool and the workpiece,selecting a minimum permitted engagement angle between the rotatingcutting tool and the workpiece, and configuring the asymmetric spiraltool path and the at least one trochoidal-like tool path relative to theworkpiece so that the engagement angle gradually varies between themaximum permitted engagement angle and the minimum permitted engagementangle.

Preferably, the configuring includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time.Preferably, the configuring also includes gradually changing the feedspeed of the tool corresponding to the changing engagement angle.Preferably, the configuring is also operative to maintain a generallyconstant work load on the tool. Preferably, the configuring is alsooperative to minimize the cost of fabricating the object, whereby thecost is a combination of the cost of operating the machine for theduration of the fabrication and the cost of the wear inflicted on thetool during the fabrication.

Preferably, the asymmetric spiral tool path includes a plurality ofspiral tool path segments, the at least one trochoidal-like tool pathincludes a plurality of trochoidal-like tool path segments, configuringan asymmetric spiral tool path includes recursively configuring each ofthe spiral tool path segments and configuring at least onetrochoidal-like tool path includes recursively configuring each of thetrochoidal-like tool path segments, and wherein responsive toconsideration of at least one of characteristics of the computernumerically controlled machine, rotating cutting tool and material ofthe workpiece, the configuring each of the tool path segments alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost ofmachining the each of the tool path segments, whereby the cost is acombination of the cost of operating the machine for the duration of themachining and the cost of the wear inflicted on the tool during themachining.

Additionally, each of the tool path segments includes a plurality oftool path subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

Preferably, the asymmetric spiral tool path is one of a convergingspiral tool path and a diverging spiral tool path.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-controlledmachine to fabricate an object from a workpiece, the machine including acontroller operative for selecting a region of the workpiece to beremoved by a rotating cutting tool, selecting a first portion of theregion to be removed by an asymmetric spiral tool path and for directingthe rotating cutting tool along at least one trochoidal-like tool pathin the region of the workpiece, and wherein the selecting a firstportion of the region is operative to minimize the machining timenecessary to remove the region.

There is yet further provided in accordance with still another preferredembodiment of the present invention an object fabricated from aworkpiece machined using a computer controlled machine tool by selectinga region of the workpiece to be removed by a rotating cutting tool,selecting a first portion of the region to be removed by an asymmetricspiral tool path and by directing the rotating cutting tool along atleast one trochoidal-like tool path in the region of the workpiece, andwherein the selecting a first portion of the region is operative tominimize the machining time necessary to remove the region.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-implementedmethod for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece by removingportions of the workpiece which are not to be included in the object,the method including the steps of considering the cross section of adesired object to be fabricated from a workpiece, defining isolatedregions of the cross section on the workpiece surface which are not tobe removed as islands, commencing configuring of a tool path in a regionnot having islands, and upon the tool path encountering an island,configuring a moat tool path which defines a moat surrounding theisland.

Preferably, the method also includes defining a composite regionincluding the island, the moat surrounding the island and regionsalready removed from the workpiece as a removed region and configuring atool path to remove a remaining region of the workpiece, which remainingregion does not include the removed region.

Preferably, the method also includes selecting a maximum permittedengagement angle between a tool and the workpiece, selecting a minimumpermitted engagement angle between the tool and the workpiece andconfiguring the moat tool path relative to the workpiece so that theengagement angle gradually varies between the maximum permittedengagement angle and the minimum permitted engagement angle.

Preferably, responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool and minimizing the cost offabricating the object, whereby the cost is a combination of the cost ofoperating the machine for the duration of the fabrication and the costof the wear inflicted on the tool during the fabrication.

Additionally, the tool paths include a plurality of tool path segmentsand configuring the tool paths includes recursively configuring each ofthe tool path segments, and wherein responsive to consideration of atleast one of characteristics of the computer numerically controlledmachine, rotating cutting tool and material of the workpiece, theconfiguring each of the tool path segments also includes minimizing,subject to other constraints, the rate of change of the engagement angleover time, gradually changing the feed speed of the tool correspondingto the changing engagement angle, maintaining a generally constant workload on the tool, and minimizing the cost of machining the each of thetool path segments, whereby the cost is a combination of the cost ofoperating the machine for the duration of the machining and the cost ofthe wear inflicted on the tool during the machining.

Additionally, each of the tool path segments includes a plurality oftool path subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

There is yet further provided in accordance with still another preferredembodiment of the present invention a method for machining a workpieceemploying a computer controlled machine tool, the method includingconsidering the cross section of a desired object to be fabricated froma workpiece, defining isolated regions of the cross section on theworkpiece surface which are not to be removed as islands, initiallydirecting the tool along a tool path in a region not having islands, andupon the tool path encountering an island, directing the tool along amoat tool path which defines a moat surrounding the island.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-implementedapparatus for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece, theapparatus including a tool path configuration engine operative forconsidering the cross section of a desired object to be fabricated froma workpiece, defining isolated regions of the cross section on theworkpiece surface which are not to be removed as islands, commencingconfiguring of a tool path in a region not having islands, and upon thetool path encountering an island, for configuring a moat tool path whichdefines a moat surrounding the island.

Preferably, the configuration engine is also operative for defining acomposite region including the island, the moat surrounding the islandand regions already removed from the workpiece as a removed region andfor configuring a tool path to remove a remaining region of theworkpiece, which remaining region does not include the removed region.

Preferably, the configuration engine is also operative for selecting amaximum permitted engagement angle between a tool and the workpiece,selecting a minimum permitted engagement angle between the tool and theworkpiece and for configuring the moat tool path relative to theworkpiece so that the engagement angle gradually varies between themaximum permitted engagement angle and the minimum permitted engagementangle.

Preferably, responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost offabricating the object, whereby the cost is a combination of the cost ofoperating the machine for the duration of the fabrication and the costof the wear inflicted on the tool during the fabrication.

Additionally, the tool paths include a plurality of tool path segmentsand configuring tool paths includes recursively configuring each of thetool path segments, and wherein responsive to consideration of at leastone of characteristics of the computer numerically controlled machine,rotating cutting tool and material of the workpiece, the configuringeach of the tool path segments also includes minimizing, subject toother constraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsegments, whereby the cost is a combination of the cost of operating themachine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

Additionally, each of the tool path segments includes a plurality oftool path subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-controlledmachine to fabricate an object from a workpiece, the machine including acontroller operative for considering the cross section of a desiredobject to be fabricated from a workpiece, defining isolated regions ofthe cross section on the workpiece surface which are not to be removedas islands, and for initially directing the tool along a tool path in aregion not having islands, and upon the tool path encountering anisland, for directing the tool along a tool path which defines a moatsurrounding the island.

There is yet further provided in accordance with still another preferredembodiment of the present invention an object fabricated from aworkpiece machined using a computer controlled machine tool byconsidering the cross section of a desired object to be fabricated froma workpiece, defining isolated regions of the cross section on theworkpiece surface which are not to be removed as islands, initiallydirecting the tool along a tool path in a region not having islands, andupon the tool path encountering an island, directing the tool along atool path which defines a moat surrounding the island.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-implementedmethod for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece by removingportions of the workpiece which are not to be included in the object,the method including the steps of identifying at least one open regionfor which a first machining time needed to remove the region is longerthan a second machining time needed to divide the region into twoindependent regions by removing a separating channel by a rotatingcutting tool between the two independent regions and removing the twoindependent regions, and defining in the region at least one separatingchannel extending between two points on edges of an external boundary ofthe region, thereby dividing the region into at least two independentregions.

Preferably, the method also includes configuring at least onetrochoidal-like tool path for the rotating cutting tool in theseparating channel which is removed by the tool moving along thetrochoidal-like tool path.

Preferably, the method also includes selecting a maximum permittedengagement angle between a rotating cutting tool and the workpiece,selecting a minimum permitted engagement angle between the rotatingcutting tool and the workpiece, and configuring the at least onetrochoidal-like tool path relative to the workpiece so that theengagement angle gradually varies between the maximum permittedengagement angle and the minimum permitted engagement angle.

Additionally, responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool and minimizing the cost offabricating the object, whereby the cost is a combination of the cost ofoperating the machine for the duration of the fabrication and the costof the wear inflicted on the tool during the fabrication.

Preferably, the at least one trochoidal-like tool path includes aplurality of trochoidal-like tool path segments and configuring at leastone trochoidal-like tool path includes recursively configuring each ofthe trochoidal-like tool path segments, and wherein responsive toconsideration of at least one of characteristics of the computernumerically controlled machine, rotating cutting tool and material ofthe workpiece, the configuring each of the tool path segments alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost ofmachining the each of the tool path segments, whereby the cost is acombination of the cost of operating the machine for the duration of themachining and the cost of the wear inflicted on the tool during themachining.

Additionally, each of the tool path segments includes a plurality oftool path subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

There is yet further provided in accordance with still another preferredembodiment of the present invention a method for machining a workpieceemploying a computer controlled machine tool, the method includingidentifying at least one open region for which a first machining timeneeded to remove the region is longer than a second machining timeneeded to divide the region into two independent regions by removing aseparating channel by a rotating cutting tool between the twoindependent regions and removing the two independent regions, anddirecting the tool along a trochoidal-like tool path in the at least oneseparating channel extending between two points on edges of an externalboundary of the region, thereby dividing the region into at least twoindependent regions.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-implementedapparatus for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece by removingportions of the workpiece which are not to be included in the object,the apparatus including a tool path configuration engine operative foridentifying at least one open region for which a first machining timeneeded to remove the region is longer than a second machining timeneeded to divide the region into two independent regions by removing aseparating channel by a rotating cutting tool between the twoindependent regions and removing the two independent regions, and fordefining in the region at least one separating channel extending betweentwo points on edges of an external boundary of the region, therebydividing the region into at least two independent regions.

Preferably, the tool path configuration engine is also operative forconfiguring at least one trochoidal-like tool path for the rotatingcutting tool in the separating channel which is removed by the toolmoving along the trochoidal-like tool path.

Additionally, the configuring includes selecting a maximum permittedengagement angle between a rotating cutting tool and the workpiece,selecting a minimum permitted engagement angle between the rotatingcutting tool and the workpiece, and configuring the at least onetrochoidal-like tool path relative to the workpiece so that theengagement angle gradually varies between the maximum permittedengagement angle and the minimum permitted engagement angle.

Additionally, responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path segments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of fabricating the object, whereby thecost is a combination of the cost of operating the machine for theduration of the fabrication and the cost of the wear inflicted on thetool during the fabrication.

Additionally, the at least one trochoidal-like tool path includes aplurality of trochoidal-like tool path segments and the configuring atleast one trochoidal-like tool path includes recursively configuringeach of the trochoidal-like tool path segments, and wherein responsiveto consideration of at least one of characteristics of the computernumerically controlled machine, rotating cutting tool and material ofthe workpiece, the configuring each of the tool path segments alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost ofmachining the each of the tool path segments, whereby the cost is acombination of the cost of operating the machine for the duration of themachining and the cost of the wear inflicted on the tool during themachining.

Additionally, each of the tool path segments includes a plurality oftool path subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-controlledmachine to fabricate an object from a workpiece, the machine including acontroller operative for identifying at least one open region for whicha first machining time needed to remove the region is longer than asecond machining time needed to divide the region into two independentregions by removing a separating channel by a rotating cutting toolbetween the two independent regions and removing the two independentregions, and for directing the tool along a trochoidal-like tool path inthe at least one separating channel extending between two points onedges of an external boundary of the region, thereby dividing the regioninto at least two independent regions.

There is yet further provided in accordance with still another preferredembodiment of the present invention an object fabricated from aworkpiece machined using a computer controlled machine tool byidentifying at least one open region for which a first machining timeneeded to remove the region is longer than a second machining timeneeded to divide the region into two independent regions by removing aseparating channel by a rotating cutting tool between the twoindependent regions and removing the two independent regions, anddefining in the region at least one separating channel extending betweentwo points on edges of an external boundary of the region, therebydividing the region into at least two independent regions.

Preferably, the object is fabricated also by directing the rotatingcutting tool along at least one trochoidal-like tool in the separatingchannel which is removed by the tool moving along the trochoidal-liketool path.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-implementedmethod for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece by removingportions of the workpiece which are not to be included in the object,and including the steps of identifying at least one semi-open region forwhich a first machining time needed to remove the region by employing atrochoidal-like tool path is longer than a second machining time neededto isolate the region by removing separating channels between the regionand all closed external boundary segments of the region and removing theremainder of the region, and defining in the region to be removed atleast one separating channel between the region and all closed externalboundary segments of the region, thereby defining a remaining openregion to be removed.

Preferably, the method also includes configuring at least onetrochoidal-like tool path for the rotating cutting tool in theseparating channel which is removed by the tool moving along the atleast one trochoidal-like tool path.

Preferably, the method also includes selecting a maximum permittedengagement angle between a rotating cutting tool and the workpiece,selecting a minimum permitted engagement angle between the rotatingcutting tool and the workpiece, and configuring the at least onetrochoidal-like tool path relative to the workpiece so that theengagement angle gradually varies between the maximum permittedengagement angle and the minimum permitted engagement angle.

Additionally, responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost offabricating the object, whereby the cost is a combination of the cost ofoperating the machine for the duration of the fabrication and the costof the wear inflicted on the tool during the fabrication.

Preferably, the at least one trochoidal-like tool path includes aplurality of trochoidal-like tool path segments and the configuring atleast one trochoidal-like tool path includes recursively configuringeach of the trochoidal-like tool path segments, and wherein responsiveto consideration of at least one of characteristics of the computernumerically controlled machine, rotating cutting tool and material ofthe workpiece, the configuring each of the tool path segments alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost ofmachining the each of the tool path segments, whereby the cost is acombination of the cost of operating the machine for the duration of themachining and the cost of the wear inflicted on the tool during themachining.

Additionally, each of the tool path segments includes a plurality oftool path subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

There is yet further provided in accordance with still another preferredembodiment of the present invention a method for machining a workpieceemploying a computer controlled machine tool, the method includingidentifying at least one semi-open region for which a first machiningtime needed to remove the region by employing a trochoidal-like toolpath is longer than a second machining time needed to isolate the regionby removing separating channels between the region and all closedexternal boundary segments of the region and removing the remainder ofthe region, and defining in the region to be removed at least oneseparating channel between the region and all closed external boundarysegments of the region, thereby defining a remaining open region to beremoved.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-implementedapparatus for generating commands for controlling a computer numericalcontrolled machine to fabricate an object from a workpiece by removingportions of the workpiece which are not to be included in the object,the apparatus including a tool path configuration engine operative foridentifying at least one semi-open region for which a first machiningtime needed to remove the region by employing a trochoidal-like toolpath is longer than a second machining time needed to isolate the regionby removing separating channels between the region and all closedexternal boundary segments of the region and removing the remainder ofthe region, and for defining in the region to be removed at least oneseparating channel between the region and all closed external boundarysegments of the region, thereby defining a remaining open region to beremoved.

Preferably, the tool path configuration engine is also operative forconfiguring at least one trochoidal-like tool path for the rotatingcutting tool in the separating channel which is removed by the toolmoving along the trochoidal-like tool path.

Additionally, the configuring includes selecting a maximum permittedengagement angle between a rotating cutting tool and the workpiece,selecting a minimum permitted engagement angle between the rotatingcutting tool and the workpiece, and configuring the at least onetrochoidal-like tool path relative to the workpiece so that theengagement angle gradually varies between the maximum permittedengagement angle and the minimum permitted engagement angle.

Preferably, responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path segments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of fabricating the object, whereby thecost is a combination of the cost of operating the machine for theduration of the fabrication and the cost of the wear inflicted on thetool during the fabrication.

Additionally, the at least one trochoidal-like tool path includes aplurality of trochoidal-like tool path segments and the configuring atleast one trochoidal-like tool path includes recursively configuringeach of the trochoidal-like tool path segments, and wherein responsiveto consideration of at least one of characteristics of the computernumerically controlled machine, rotating cutting tool and material ofthe workpiece, the configuring each of the tool path segments alsoincludes minimizing, subject to other constraints, the rate of change ofthe engagement angle over time, gradually changing the feed speed of thetool corresponding to the changing engagement angle, maintaining agenerally constant work load on the tool, and minimizing the cost ofmachining the each of the tool path segments, whereby the cost is acombination of the cost of operating the machine for the duration of themachining and the cost of the wear inflicted on the tool during themachining.

Additionally, each of the tool path segments includes a plurality oftool path subsegments and recursively configuring each of the tool pathsegments includes recursively configuring each of the tool pathsubsegments, and wherein responsive to consideration of at least one ofcharacteristics of the computer numerically controlled machine, rotatingcutting tool and material of the workpiece, the configuring each of thetool path subsegments also includes minimizing, subject to otherconstraints, the rate of change of the engagement angle over time,gradually changing the feed speed of the tool corresponding to thechanging engagement angle, maintaining a generally constant work load onthe tool, and minimizing the cost of machining the each of the tool pathsubsegments, whereby the cost is a combination of the cost of operatingthe machine for the duration of the machining and the cost of the wearinflicted on the tool during the machining.

There is yet further provided in accordance with still another preferredembodiment of the present invention an automated computer-controlledmachine to fabricate an object from a workpiece, the machine including acontroller operative for identifying at least one semi-open region forwhich a first machining time needed to remove the region by employing atrochoidal-like tool path is longer than a second machining time neededto isolate the region by removing separating channels between the regionand all closed external boundary segments of the region and removing theremainder of the region, and for directing the tool along atrochoidal-like tool path in the at least one separating channel betweenthe region and all closed external boundary segments of the region,thereby defining a remaining open region to be removed.

There is yet further provided in accordance with still another preferredembodiment of the present invention an object fabricated from aworkpiece machined using a computer controlled machine tool byidentifying at least one semi-open region for which a first machiningtime needed to remove the region by employing a trochoidal-like toolpath is longer than a second machining time needed to isolate the regionby removing separating channels between the region and all closedexternal boundary segments of the region and removing the remainder ofthe region, and by defining in the region to be removed at least oneseparating channel between the region and all closed external boundarysegments of the region, thereby defining a remaining open region to beremoved.

Preferably, the object is fabricated also by directing the rotatingcutting tool along at least one trochoidal-like tool in the separatingchannel which is removed by the tool moving along the trochoidal-liketool path.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be understood and appreciated more fully fromthe following detailed description, taken in conjunction with thedrawings in which:

FIGS. 1A-1S-2 are together a series of simplified illustrations whichare helpful in understanding the invention;

FIGS. 2A-2L-2 are together another series of simplified illustrationswhich are helpful in understanding the invention;

FIGS. 3A-3D are simplified screen shots illustrating some aspects of thepresent invention; and

FIGS. 4A and 4B are simplified illustrations of details of functionalityillustrated more generally in certain ones of FIGS. 1A-1S-2 and FIGS.2A-2L-2.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

The present invention relates to various aspects of an automatedcomputer-implemented method for generating commands for controlling acomputer numerical controlled (CNC) machine to fabricate an object froma stock material, various aspects of a method for machining the stockmaterial which employs the above commands, automatedcomputer-implemented apparatus for generating the above commands, anumerically-controlled machine operative to fabricate an object from astock material by using the above commands, and an object fabricated byusing the above commands.

The invention, in its various aspects, is described hereinbelow withrespect to a series of drawings, which initially illustrate an exampleof an object to be fabricated, a simulated overlay of the object on astock material to be machined and sequences of machining steps that areproduced by commands generated in accordance with the present invention.It is appreciated that although sequential machining steps areillustrated, the invention is not limited to a machining method butextends as noted above to the generation of the commands, the apparatus,which generates them, the apparatus which carries them out and to theresult produced thereby.

The term “calculation” is used throughout to refer to the generation ofcommands which produce sequences of machining steps to be employed inthe machining of a particular region of the stock material. Thedefinitions “calculate”, “calculation” and calculation are ofcorresponding meaning.

FIGS. 1A and 1B are respective pictorial and top view illustrations ofan object 100 which is an example of objects that can be fabricated inaccordance with the present invention. The configuration of the object100 is selected to illustrate various particular features of the presentinvention. It is noted that any suitable three-dimensional object thatcan be machined by a conventional 3-axis CNC machine tool may befabricated in accordance with a preferred embodiment of the presentinvention.

As seen in FIGS. 1A & 1B, the object 100 is seen to have a generallyplanar base portion 102 from which five protrusions, here designated byreference numerals 104, 106, 108, 110 and 112 extend. FIG. 1C showsstock material 114 overlaid by an outline of object 100.

In accordance with a preferred embodiment of the present invention, atool path designer, using the automated computer-implemented method forgenerating commands for controlling a computer numerical controlledmachine of the present invention, accesses a CAD drawing of the object100 in a standard CAD format, such as SOLIDWORKS®. He selects a specificmachine tool to be used in fabrication of the object 100 from a menu andselects a specific rotating cutting tool to carry out each machiningfunction required to fabricate the object.

For the sake of simplicity, the illustrated object 100 is chosen to bean object that can be fabricated by a single machining function, itbeing appreciated that the applicability of the present invention is notlimited to objects which can be fabricated by a single machiningfunction.

The tool path designer then defines the geometry of the stock materialto be used in fabrication of the object 100. This may be doneautomatically by the automated computer-implemented apparatus of thepresent invention or manually by the tool path designer. The tool pathdesigner then specifies the material which constitutes the stockmaterial, for example, INCONEL® 718. The present invention utilizes thechoice of machine tool, rotating cutting tool and the material by thetool path designer to calculate various operational parameters, based oncharacteristics of the machine tool, rotating cutting tool and material.

In accordance with a preferred embodiment of the present invention, aseries of display screens are employed to provide a display for the toolpath designer, indicating the various operational parameters, such asminimum and maximum surface cutting speed, minimum and maximum chipthickness, minimum and maximum feed speed, minimum and maximum spindlerotational speed, minimum and maximum engagement angles between therotating cutting tool and the workpiece, axial depth of cut, machiningaggressiveness level. An example of such a series of display screensappears in FIGS. 3A-3D.

The tool path designer is given limited latitude in changing some of theparameters, such as particularly, the machining aggressiveness level.Preferably, the tool path designer may also instruct the system toselect parameters for which, for example, optimization of machiningtime, wear inflicted on the cutting tool, machining cost or anycombination thereof is achieved. It is appreciated that although forsome of the operational parameters described hereinabove a range ofvalues is displayed to the tool path designer, the present inventionalso calculates an optimal operational value for all of the operationalparameters to be employed.

Once all of the parameters appearing on the screen, such as the displayscreens of FIGS. 3A-3D, are finalized, a tool path for machining theworkpiece is calculated in accordance with a preferred embodiment of thepresent invention. The calculation of a tool path in accordance with apreferred embodiment of the present invention is described hereinbelowwith reference to FIGS. 1A-1S-2 which illustrate the actual progressionof tool path in stock material 114.

It is a particular feature of the present invention that the tool pathis calculated recursively, whereby initially a first tool path segmentof the tool path is calculated for an initial region of the workpiece,and thereafter a subsequent sequential tool path segment of the toolpath is similarly calculated for an initial region of a remaining regionof the workpiece. Additional subsequent sequential tool path segmentsare similarly calculated, until a tool path for machining the entireworkpiece to the desired object has been calculated.

Initially, a first cross section of the stock material having theoutline of the object 100 overlaid thereon and having a depth equal tothe designated axial depth of cut is calculated. This cross section isillustrated schematically in FIG. 1D and is designated by referencenumeral 116. Cross section 116 is characterized as having an externalboundary 118 and a plurality of islands 105, 107, 109, 111 and 113respectively corresponding to the cross sections of protrusions 104,106, 108, 110 and 112 at the depth of cross section 116. It isappreciated that islands 105, 107, 109, 111 and 113 are offsetexternally to the cross sections of protrusions 104, 106, 108, 110 and112 by a distance which is generally a bit larger than the radius of therotating cutting tool, thereby when machining a tool path whichcircumvents the islands, a narrow finishing width remains to be finishmachined at a later stage.

It is appreciated that the axial depth of cross section 116 constitutesa first step down which is a first phase in the machining of object 100.Throughout, the term “step down” is used to describe a single machiningphase at a constant depth. As shown in FIG. 1C, the complete machiningof object 100 requires two additional step downs corresponding to crosssections 119 and 120. Therefore, subsequent to the calculation of crosssection 116, a second step down and thereafter a third step down arecalculated, corresponding to cross sections 119 and 120. Preferably, thevertical distance between subsequent step downs is generally between 1and 4 times the diameter of the rotating cutting tool.

In accordance with a preferred embodiment of the present invention, amachining region is initially automatically identified in cross section116. There are preferably three types of machining regions which areclassified by the characteristics of their exterior boundaries.Throughout, a segment of the boundary of a region through which theregion can be reached by a rotating cutting tool from the outside of theregion by horizontal progression of the rotating cutting tool is termedan “open edge”. All other boundary segments are termed throughout as“closed edges”.

The three types of machining regions are classified as follows:

Type I—an open region characterized in that the entire exterior boundaryof the region consists solely of open edges;

Type II—a semi-open region characterized in that the exterior boundaryof the region consists of both open edges and closed edges;

Type III—a closed region characterized in that the entire exteriorboundary of the region consists solely of closed edges;

Preferably, a tool path to be employed in machining a region iscalculated to comprise one or more tool path segments, wherein each toolpath segment is one of a converging spiral tool path segment, atrochoidal-like tool path segment and a diverging spiral tool pathsegment. Generally, a converging spiral tool path segment is preferredwhen machining a Type I region, a trochoidal-like tool path segment ispreferred when machining a Type II region, and a diverging spiral toolpath is preferred when machining a Type III region.

The term “trochoidal-like” is used throughout to mean a trochoidal toolpath or a modification thereof that retains a curved cutting path and areturn path which could be either curved or generally straight.

As known to persons skilled in the art, the machining of spiral toolpath segments is generally more efficient with respect to the amount ofmaterial removed per unit of time than the machining of trochoidal-liketool path segments for generally similar average stepovers. Therefore,the present invention seeks to maximize the area to be machined byspiral tool path segments.

A converging spiral tool path segment calculated to machine a Type Iregion preferably is a tool path segment which spirals inwardly from anexternal boundary of the region to an internal contour. The internalcontour is preferably calculated as follows:

In a case where there are no islands within the external boundary of theType I region, the internal contour is preferably calculated to be asmall circle having a radius which is generally smaller than the radiusof the cutting tool, and which is centered around the center of area ofthe region;

In a case where there is one island within the external boundary of theType I region, and the shortest distance between the one island and theexternal boundary of the Type I region is longer than a selectedfraction of the diameter of the rotating cutting tool, the internalcontour is preferably calculated to be generally alongside the externalboundary of the island; and

In a case where:

-   -   there is one island within the external boundary of the Type I        region and the shortest distance between the single island and        the external boundary of the Type I region is shorter than a        selected fraction of the diameter of the rotating cutting tool;        or    -   there is more than one island within the external boundary of        the Type I region        the internal contour is preferably calculated to be a contour        which is offset interiorly to the external boundary of the        region by a distance which is generally equal to 1.5 radii of        the rotating cutting tool.

Once the internal contour is calculated, it is automatically verifiedthat the internal contour does not self intersect. In a case where theinternal contour does self intersect at one or more locations,preferably a bottleneck is identified in the vicinity of each such selfintersection. If the bottleneck does not overlap with an island, aseparating channel is preferably calculated at each such bottleneck. Aseparating channel preferably divides the region into two Type I regionswhich can be machined independently of each other by separate convergingspiral tool path segments. If the bottleneck does overlap with anisland, the internal contour is preferably recalculated to be offsetinteriorly to the external boundary by generally half of the originaloffset. This process is repeated until an internal contour which doesnot self-intersect is calculated.

It is a particular feature of the present invention that a convergingspiral tool path segment which spirals inwardly from an externalboundary of a region to an internal contour is calculated to be a“morphing spiral”. The term “morphing spiral” is used throughout to meana spiral tool path segment which gradually morphs the geometrical shapeof one boundary or contour to the geometrical shape of a second boundaryor contour as the spiral tool path segment spirals therebetween. Whilevarious methods of morphing are known to persons skilled in the art, thepresent invention seeks to implement particular methods of morphing inaccordance with preferred embodiments of the present invention, asdescribed hereinbelow.

It is another particular feature of the present invention that theengagement angle of the cutting tool employed throughout the tool pathsegment is not fixed, but rather may vary between the predeterminedminimum and maximum engagement angles over the course of the tool pathsegment. This varying of the engagement angle allows for varyingstepovers over the course of the tool path segment, and thereby enablesthe tool path segment to morph between two generally dissimilargeometrical shapes. The term “stepover” is used throughout to designatethe distance between sequential loops of a spiral tool path segment. Itis appreciated that the cutting tool efficiency which is achieved byemploying a morphing spiral tool path segment is generally significantlygreater than the cutting tool efficiency which is achieved by employinga trochoidal-like tool path segment. It is also appreciated that whereappropriate, an engagement angle which is generally close to the maximumengagement angle is preferred.

While it is appreciated that employing varying engagement angles overthe course of a tool path segment may have a negative impact ofincreasing the wear of the cutting tool due to the varying mechanicalload on the cutting tool and to chip thinning, it is a particularfeature of the present invention that this negative impact is generallycompensated for by automatically dynamically adjusting the feed velocityto correspond to the varying engagement angle. It is another particularfeature of the present invention that the engagement angle is variedgradually over the course of the tool path segment, thereby preventingsudden and sharp changes in cutting tool load, and thereby furtherreducing excess wear of the cutting tool.

Returning now to the calculation of a converging spiral tool pathsegment employed to machine a Type I region, once an internal contourhas been calculated, the number of loops to be included in a convergingspiral tool path segment which spirals inwardly from the externalboundary of the region to the internal contour is calculated preferablyas illustrated in FIG. 4A.

As shown in FIG. 4A, a plurality of bridges 500 of a predefined densityare each stretched from the internal contour 502 to the externalboundary 504. A bridge point 506 of each of bridges 500 is initiallydefined as the point of intersection of bridge 500 with externalboundary 504. The length of the shortest bridge divided by the minimumstepover is generally equal to the maximum number of loops that can beincluded in the spiral tool path segment. The length of the longestbridge divided by the maximum stepover is generally equal to the minimumnumber of loops which must be included in the spiral tool path. Asdescribed hereinabove, minimum and maximum engagement angles aredetermined based on information provided by the tool path designer,which angles determine the minimum and maximum stepover of the spiraltool path segment.

It is appreciated that the furthest distance, in any direction, frominternal contour 502 which can be machined by a converging spiral toolpath segment is the number of loops included in the converging spiraltool path segment multiplied by the maximum stepover. Areas betweeninternal contour 502 and external boundary 504 beyond this furthestdistance from the internal contour cannot be machined by the convergingspiral tool path segment, and are therefore preferably machined byclipping prior to the machining of the converging spiral tool pathsegment. Throughout, the term “clipping” is used to define thecalculation of machining of areas of a region which cannot be machinedby an optimal spiral tool path segment. Typically, clipped areas aremachined either by a trochoidal-like tool path segment, before themachining of the spiral tool path segment, or by machining a separatingchannel which separates the clipped area from the remainder of theregion and by subsequently machining the separated clipped areaseparately by a spiral tool path segment.

Throughout, a parameter ‘n’ will be used to designate a possible numberof loops to be included in a spiral tool path segment, wherein n is anumber between the minimum number of loops which must be included in thespiral tool path segment and the maximum number of loops that can beincluded in the spiral tool path segment.

For each possible value of n, a first work time for a first machiningmethod needed to machine the area between external boundary 504 andinternal contour 502 is calculated by summing the time needed to machinethe spiral tool path segment and the time needed to machine all clippedareas which were identified between external boundary 504 and internalcontour 502 as described hereinabove. The optimal number of loops to beincluded in the spiral tool path segment is chosen to be the value of nfor which the first calculated work time is the shortest.

In a case where the internal contour is calculated to be a small circlewhich is centered around the center of area of the region, a second worktime for a second machining method is calculated by summing the worktime needed to machine a separating channel extending along the shortestbridge connecting the external boundary to the internal contour, furtherextending through the small circle and then further extending along anopposite bridge up to an opposite segment of the external boundary, thusdividing the region into two independent Type I regions, and the worktime needed to machine the two independent Type I regions. In a casewhere the second work time is shorter than the first work time, thesecond machining method is preferred over the first machining method.

Once the optimal number of loops to be included in the converging spiraltool path segment is chosen, clipped areas and tool paths for theirremoval are calculated as described hereinabove. Subsequently, a newexternal boundary defined by the clipped areas is calculated and allbridge points are updated accordingly to be located on the new externalboundary. Thereafter, the actual path of the spiral tool path segment iscalculated, as follows:

Initially, the bridge point 510 of a first bridge 512 is preferablyselected as a first spiral point of spiral tool path segment 514. Firstbridge 512 is preferably selected to minimize the time required to movethe cutting tool from its previous position. A possible second spiralpoint of spiral tool path segment 514 is calculated as a point on asecond bridge 516, immediately adjacent to first bridge 512 in aclimbing direction of the cutting tool from first bridge 512, whichpoint is distanced from bridge point 517 of second bridge 516 alongsecond bridge 516 by the length of second bridge 516 divided by theremaining number of loops to be included in tool path segment 514.

For the possible second spiral point, the engagement angle at which thecutting tool will engage the material by following the spiral tool pathsegment 514 from first spiral point 510 to the possible second spiralpoint is calculated. In a case where the calculated engagement angle isbetween the predetermined minimum and maximum engagement angles, thepossible second spiral point is chosen as the second spiral point 518,and a new linear subsegment 520 between first spiral point 510 andsecond spiral point 518 is added to spiral tool path segment 514.

In a case where the engagement angle is less than the predeterminedminimum engagement angle, a binary search for a second spiral point forwhich the calculated engagement angle is generally equal to thepredetermined minimum engagement angle is performed. The binary searchis performed between the possible second spiral point and a point onsecond bridge 516 distanced from bridge point 517 of second bridge 516by the maximum stepover. Once a second spiral point 518 is found, a newlinear subsegment 520 between first spiral point 510 and second spiralpoint 518 is added to spiral tool path segment 514.

In a case where the engagement angle is greater than the predeterminedmaximum engagement angle, a binary search for a second spiral point forwhich the calculated engagement angle is generally equal to thepredetermined maximum engagement angle is performed. The binary searchis performed between bridge point 517 of the second bridge 516 and thepossible second spiral point. Once a second spiral point 518 is found, anew linear subsegment 520 between first spiral point 510 and secondspiral point 518 is added to spiral tool path segment 514.

In a case where new linear subsegment 520 intersects with internalcontour 502 of the region, the spiral tool path segment 514 isterminated at the point of intersection, possibly creating one or moreseparate unmachined residual areas generally adjacent to internalcontour 502. For each such separate residual area, if the size of theseparate residual area is larger than a predetermined small value, it iscalculated to be machined by a trochoidal-like tool path segment.

In a case where new linear subsegment 520 intersects with an island, thecalculation of spiral tool path segment 514 is terminated at the pointof intersection, and a moat is calculated to commence at the point ofintersection and circumvent the island. The remainder of the region forwhich a tool path has yet to be calculated is designated as a new Type Iregion to be calculated separately.

The term “moat” is used throughout to designate a trochoidal-like toolpath segment which machines a channel generally adjacent to an islandthat circumvents the island, thereby separating the island from theremainder of the material which needs to be machined. The width of themoat is preferably at least 2.5 times the radius of the cutting tool andpreferably at most 4 times the radius of the cutting tool. These valuesare predefined, however they may be modified by the tool path designer.It is a particular feature of the present invention that machining amoat around an island is operative to create a residual region which isof the same type as the original region. This is of particular valuewhen machining a Type I region or a Type III region which are thus ableto be generally machined by spiral tool path segments which aregenerally more efficient than trochoidal-like tool path segments.

Additionally, the machining of a moat to circumvent an island iseffective in preventing the formation of two fronts of a machined regionadjacent to the island, which may potentially form one or more longnarrow residual walls between the two fronts. As known to personsskilled in the art, the formation of narrow residual walls isundesirable as machining them may lead to damage to the cutting tooland\or to the workpiece.

Once second spiral point 518 has been calculated, the remaining numberof loops to be included in the remainder of tool path segment 514 isupdated. It is appreciated that the remaining number of loops may be amixed number. The subsequent segments of the remainder of spiral toolpath segment 514 are calculated recursively, whereby second spiral point518 is designated to be a new first point of the remainder of spiraltool path segment 514, and the bridge 530 immediately adjacent to secondbridge 516 in a climbing direction of the cutting tool from secondbridge 516 is designated to be a new second bridge. Additionally, secondspiral point 518 is designated as a new bridge point of second bridge516, and the remaining region to be machined is recalculated.

The machining of a Type II region is calculated as follows:

Initially, a spiral machining time is calculated as the sum of themachining time needed for machining separating channels adjacent to allclosed edges of the Type II region and the machining time needed formachining the remaining area of the region by a converging spiral toolpath segment. Additionally, a trochoidal-like machining time iscalculated as the machining time needed for machining the entire Type IIregion by a trochoidal-like tool path segment. If the spiral machiningtime is shorter than the trochoidal-like machining time, separatingchannels are calculated adjacent to all closed edges of the region, andthe remaining separated area is calculated to be machined by aconverging spiral tool path segment. If the spiral machining time islonger than the trochoidal-like machining time, a trochoidal-like toolpath segment is calculated as follows:

The longest open edge of the region is selected as the “front” of theregion. The remainder of the exterior boundary of the region is definedas the “blocking boundary”. A starting end is selected as one of the twoends of the front, for which when machining along the front from thestarting end to the opposite end would result in a climb milling toolpath.

As shown in FIG. 4B a plurality of bridge lines 550 of a predefineddensity are each stretched from a front 552 across the region towards ablocking boundary 554. A bridge point 556 of each of bridges 550 isinitially defined as the point of intersection of each of bridges 550with front 552. A starting end 560 and an opposite end 562 are selectedso that bridges 550 are ordered from starting end 560 to opposite end562 in a climbing direction of the cutting tool. A single opentrochoidal-like tool path segment 564 for machining an area adjacent tofront 552 having a width which is generally equal to the maximumstepover is calculated by selecting a suitable point on each of bridges550 and interconnecting the suitable points in the order of bridge lines550 between starting end 560 and opposite end 562, as follows:

Initially, starting end 560 is preferably selected as a first point ofthe single trochoidal-like tool path segment 564. A possible secondpoint of the trochoidal-like tool path segment 564 is calculated as apoint on a first bridge 570, immediately adjacent to first point 560 ina climbing direction of the cutting tool from first point 560, whichpossible second point is distanced from bridge point 572 of the firstbridge by the larger of the maximum stepover and the length of firstbridge 570. In the illustrated example of FIG. 4B, the possible secondpoint is calculated to be at the intersection 574 of first bridge 572and blocking boundary 554.

For the possible second point, the engagement angle at which the cuttingtool will engage the material by following the cutting tool path fromthe first point to the possible second point is calculated. In a casewhere the calculated engagement angle is between the predeterminedminimum and maximum engagement angles, the possible second point ischosen as the second point, and a new linear subsegment between firstpoint 560 and the second point is added to the single trochoidal-likecutting tool path segment 564.

In a case where the engagement angle is less than the predeterminedminimum engagement angle, a binary search for a second point for whichthe calculated engagement angle is generally equal to the predeterminedminimum engagement angle is performed. The binary search is performedbetween the possible second point and a point on first bridge 570distanced from bridge point 572 of first bridge 570, along first bridge570, by the larger of the maximum stepover and the length of firstbridge 570. Once a second point is found, a new linear subsegmentbetween first point 560 and the second point is added to the singletrochoidal-like cutting tool path segment 564.

In a case where the engagement angle is greater than the predeterminedmaximum engagement angle, a binary search for a second point for whichthe calculated engagement angle is generally equal to the predeterminedmaximum engagement angle is performed. The binary search is performedbetween bridge point 572 of first bridge 570 and the possible secondpoint. Once a second point is found, a new linear subsegment betweenfirst point 560 and the second point is added to the singletrochoidal-like cutting tool path segment 564.

In the illustrated example of FIG. 4B, intersection 574 is selected asthe second point, and a new linear subsegment 580 between first point560 and second point 574 is added to the single trochoidal-like cuttingtool path segment 564.

Subsequently, calculation of the remainder of the single trochoidal-liketool path segment 564 is achieved by recursively performing theaforementioned calculation of tool path subsegments through suitablepoints on ordered bridges 550 up until opposite end 562 of selectedfront 552. In a case where the single trochoidal-like tool path segment564 crosses an island, the single trochoidal-like tool path segment 564is clipped at the intersecting points of the single trochoidal-like toolpath segment 564 and the external boundary of the island, therebycreating two disjoint subsegments of the single trochoidal-like toolpath segment 564. These two subsegments are then connected along asection of the external boundary of the island facing the front, whichsection is a closed edge.

The aforementioned calculation completes the calculation of a tool pathsegment for machining a part of the Type II region. At this point, theremainder of the Type II region to be machined is calculated, and a toolpath for machining of the remainder of the Type II region is calculatedrecursively as described hereinabove. It is appreciated that themachining of the remainder of the Type II region requires repositioningof the cutting tool to a starting end of a front of the remainder of theType II region. It is appreciated that repositioning techniques are wellknown to persons skilled in the art.

Referring now to the calculation of a tool path for machining of a TypeIII region, a diverging spiral tool path is preferred when machiningType III regions, as described hereinabove. A diverging spiral tool pathsegment calculated to machine a Type III region is a tool path segmentwhich spirals outwardly from an innermost contour to an externalboundary via a multiplicity of nested internal contours. The nestedinternal contours are calculated as follows:

A first nested internal contour is calculated to be a contour which isoffset interiorly to the external boundary of the region by a distancewhich is generally equal to 1.5 radii of the cutting tool. Additionalnested internal contours are then calculated recursively inwardly fromthe first nested internal contour, each nested internal contour beinginwardly spaced from the nested internal contour immediately externallyadjacent thereto by a distance which is generally equal to 1.5 radii ofthe rotating cutting tool. A last nested internal contour is calculatedto be a contour having a center of area which is closer than 1.5 radiiof the cutting tool to at least one point on the contour. Inwardly ofthe last nested internal contour, the innermost contour is calculated tobe a small circle having a radius which is generally smaller than theradius of the cutting tool, and which is centered around the center ofarea of the last nested internal offset contour.

In a case where the innermost contour is either within the externalboundary of an island or intersects with the external boundary of anisland, a moat is calculated to circumvent the island, and the innermostcontour is recalculated to be immediately external to the externalboundary of the moat, such that the innermost contour does not intersectwith any other islands. It is noted that nested internal contours whichintersect with an external boundary of any island are discarded.

Once the nested internal contours have been calculated, the number ofloops to be included in a diverging spiral tool path segment which willspiral outwardly from the innermost contour to the last nested internaloffset contour is calculated preferably as follows:

A plurality of bridge lines are stretched from the innermost contour toa next internal offset contour immediately externally adjacent thereto.A bridge point of each bridge is initially defined as the point ofintersection of the bridge with the innermost contour. The length of theshortest bridge divided by the minimum stepover provides a theoreticalmaximum of the number of loops that can be theoretically included in thediverging spiral tool path. The length of the longest bridge divided bythe maximum stepover provides an absolute minimum of the number of loopswhich must be included in the diverging spiral tool path segment that isrequired to machine the entire area between the innermost contour andthe next internal offset contour.

It is appreciated that the furthest distance, in any direction, from theinnermost contour which can be reached by a diverging spiral tool pathsegment is the number of loops included in the diverging spiral toolpath segment multiplied by the maximum stepover. Areas between theinnermost contour and the next internal offset contour beyond thisfurthest distance cannot be machined by the diverging spiral tool pathsegment, and are preferably machined by clipping after the machining ofthe diverging spiral tool path segment.

Throughout, the parameter n is used to designate a possible number ofloops to be included in the spiral tool path segment, wherein n is anumber between the minimum number of loops which must be included in thespiral tool path segment and the maximum number of loops that can beincluded in the spiral tool path segment.

For each possible value of n, the work time needed to machine the areabetween the innermost contour and the next internal offset contour iscalculated by summing the time needed to machine the spiral tool pathsegment and the time needed to machine all clipped areas which wereidentified between the innermost contour and the next internal offsetcontour as described hereinabove. The optimal value of loops to beincluded in the spiral tool path segment is chosen to be the value of nfor which the calculated work time is the shortest.

Once the optimal value of loops to be included in the tool path segmentis chosen, the actual path of the spiral tool path segment iscalculated. Initially, the bridge point of a first bridge is preferablyselected as a starting spiral point of the spiral tool path segment. Thefirst bridge is preferably selected to minimize the time required tomove the rotating cutting tool from its previous position. A possiblesecond spiral point of the spiral tool path segment is calculated as apoint on a second bridge, immediately adjacent to the first bridge in aclimbing direction of the cutting tool from the first bridge, whichpoint is distanced from the bridge point of the second bridge by thelength of the second bridge divided by the remaining number of loops tobe included in the tool path segment.

For the possible second spiral point, the engagement angle at which thecutting tool will engage the material by following the cutting tool pathfrom the first spiral point to the possible second spiral point iscalculated. In a case where the calculated engagement angle is betweenthe predetermined minimum and maximum engagement angles, the possiblesecond spiral point is chosen as the second spiral point, and a newlinear subsegment between the first spiral point and the second spiralpoint is added to the spiral cutting tool path segment.

In a case where the engagement angle is less than the predeterminedminimum engagement angle, a binary search for a second spiral point forwhich the calculated engagement angle is generally equal to thepredetermined minimum engagement angle is performed. The binary searchis performed between the possible second spiral point and a point on thesecond bridge distanced from the bridge point of the second bridge bythe maximum stepover. Once a second spiral point is found, a new linearsubsegment between the first spiral point and the second spiral point isadded to the spiral tool path segment.

In a case where the engagement angle is greater than the predeterminedmaximum engagement angle, a binary search for a second spiral point forwhich the calculated engagement angle is generally equal to thepredetermined maximum engagement angle is performed. The binary searchis performed between the bridge point of the second bridge and thepossible second spiral point. Once a second spiral point is found, a newlinear subsegment between the first spiral point and the second spiralpoint is added to the spiral tool path segment.

In a case where the new linear subsegment intersects with an island, thecalculation of the spiral tool path segment is terminated at the pointof intersection, where a moat is calculated to commence and circumventthe island. The remainder of the region for which a tool path has yet tobe calculated is designated as a new Type III region to be calculatedseparately.

In a case where the new linear subsegment intersects with the nextinternal offset contour, an additional loop of the diverging spiral toolpath segment is calculated, and the portions of the additional loopwhich are internal to the next internal offset contour define one ormore uncalculated residual regions between the diverging spiral toolpath segment and the next internal offset contour, which residualregions are each calculated as a Type II region, preferably by employinga trochoidal-like tool path segment. The portions of the additional loopwhich are internal to the next internal offset contour are connectedalong the next internal offset contour to form a continuous loop whichis the final loop of the diverging spiral tool path segment.

Once the second spiral point has been calculated, the remaining numberof loops to be included in the tool path segment is recalculated and thesubsequent segments of the spiral cutting tool path segment arecalculated recursively, whereby the second spiral point is designated tobe a new starting point of the remainder of the spiral tool pathsegment, and the bridge immediately adjacent to the second bridge in aclimbing direction of the cutting tool from the second bridge isdesignated to be the new second bridge. Additionally, the second spiralpoint is designated as the new bridge point of the second bridge, andthe remaining region to be machined is recalculated.

Subsequently, calculation of the remainder of the diverging spiral toolpath for the remainder of the region is achieved by recursivelyperforming the aforementioned calculation of diverging spiral tool pathsegments through subsequent consecutive pairs of nested internalcontours between the last nested internal offset contour and theexternal boundary of the region.

It is appreciated that all of the calculations of the tool pathsdescribed hereinabove produce piecewise linear tool paths. In caseswhere a piecewise linear tool path is not suitable for a particularworkpiece being machined by a particular CNC machine, a smoothingapproximation of the piecewise linear tool path may be calculated. Suchapproximation methods are well known to persons skilled in the art.

Returning now to the illustrated example of FIG. 1D, cross section 116is initially identified as a Type I region which includes multipleprotrusions. Therefore, a converging spiral tool path segment iscalculated between the external boundary of the workpiece and acalculated internal contour, as the initial tool path segment. Thiscalculation preferably begins with calculation of a spiral tool pathsegment which begins from a selected location just outside the peripheryof cross section 116. Reference is made in this context to FIGS. 1E-1and 1E-2, which are respective isometric and top view illustrations ofthe stock material 114 overlaid by outline 121 of object 100 in whichthe initial spiral tool path segment is indicated generally by referencenumeral 122. It is noted that the spiral tool path is indicated by solidlines, which represent the center of the rotating cutting tool, whosecross-sectional extent is designated by reference numeral 124 in FIG.1E-2. The selected location, here designated by reference numeral 126,is preferably selected to minimize the time required to move therotating cutting tool from its previous position.

In the illustrated example of FIGS. 1E-1 and 1E-2, the initial tool pathsegment is a converging spiral segment which is calculated as describedhereinabove. As shown in FIGS. 1E-1 and 1E-2, initial spiral tool pathsegment 122, ultimately intersects with island 105 at intersecting point130 at which point spiral tool path segment 122 is terminated. As shownin FIGS. 1F-1 and 1F-2, a moat 132 which circumvents island 105 iscalculated.

As shown in FIGS. 1F-1 and 1F-2, an inner boundary 134 of moat 132 iscalculated to be generally alongside the outer boundary of island 105.It is appreciated that a narrow offset remains between the island 105and an inner boundary 134 of the moat, which may be finish machined at alater stage. The outer boundary 136 of moat 132 is calculated as beingoffset from inner boundary 134 by the moat width.

As shown in FIGS. 1F-1 and 1F-2, the outer boundary 136 of moat 132intersects with island 107 at points 138 and 139. Therefore, anadditional moat 140 is calculated to circumvent island 107, wherebymoats 132 and 140 are joined to form one continuous moat whichcircumvents islands 105 and 107. As clearly shown in FIGS. 1F-1 and1F-2, the combination of the initial spiral tool path segment 122 andsubsequent moats 132 and 140 which circumvent islands 105 and 107 definea new Type I region which is designated by reference numeral 142.

Region 142 includes multiple islands 109, 111 and 113. As clearly shownin FIGS. 1F-1 and 1F-2, a bottleneck 150 is detected in region 142.Therefore, as shown in FIGS. 1G-1 and 1G-2, a separating channel 152 iscalculated at the location of bottleneck 150, effectively dividingregion 142 into two independent Type I regions designated by referencenumerals 154 and 156.

Turning now to FIGS. 1H-1 and 1H-2, it is shown that initially, a spiraltool path segment for region 154 is calculated, while the calculation ofregion 156 is deferred. As shown in FIGS. 1H-1 and 1H-2, a startingpoint 160 is chosen and a spiral tool path segment 162 extends frominitial point 160 generally along the external boundary of region 154until intersecting with island 109 at intersecting point 164 at whichpoint spiral tool path segment 162 is terminated. As shown in FIGS. 1I-1and 1I-2, a moat 166 which circumvents island 109 is calculated. Theremainder of region 154 is identified as a Type I region designated byreference numeral 170.

Region 170 includes islands 111 and 113. As clearly shown in 1I-1 and1I-2, a bottleneck 172 is detected in region 170. Therefore, as shown in1J-1 and 1J-2, a separating channel 174 is calculated at the location ofbottleneck 172, effectively dividing region 170 into two independentType I regions designated by reference numerals 176 and 178.

Turning now to 1K-1 and 1K-2, it is shown that initially, a spiral pathfor machining region 176 is calculated, while the calculation of region178 is deferred. As shown in FIGS. 1K-1 and 1K-2, region 176 does notinclude any islands, therefore a converging spiral tool path segment iscalculated to machine region 176 with the internal boundary of region176 being a small circle 177 of a radius which is generally smaller thanthe radius of the tool, and which is centered around the center of areaof region 176.

Subsequently, a spiral tool path segment for region 178 is calculated.As shown in FIGS. 1L-1 and 1L-2, a starting point 180 is chosen and aspiral tool path segment 182 is extended from initial point 180generally along the external boundary of region 178 until intersectingwith island 111 at intersecting point 184 at which point spiral toolpath segment 182 is terminated. As shown in FIGS. 1M-1 and 1M-2, a moat186 which circumvents protrusion 110 is calculated.

It is appreciated that in a case where the external boundary of a moatis calculated to be in close proximity to the external boundary of theType I region which includes the moat, a local widening of the moat iscalculated to prevent the forming of a narrow residual wall between themoat and the external boundary of the region. As known to personsskilled in the art, the formation of narrow residual walls isundesirable as machining them may lead to damage to the cutting tool and\ or to the workpiece.

As seen in FIGS. 1M-1 and 1M-2, the external boundary of moat 186 iscalculated to be in close proximity to the external boundary of region178. Therefore, moat 186 is locally widened up to the external boundaryof region 178, along a narrow residual wall area 189 in which, withoutthis widening, a narrow residual wall would be have been formed betweenmoat 186 and the external boundary of region 178. Locally widened moat186 divides region 178 into two independent Type I regions designated byreference numerals 190 and 192.

Turning now to FIGS. 1N-1 and 1N-2, it is shown that initially, region190 is calculated, while the calculation of region 192 is deferred. Asshown in FIGS. 1N-1 and 1N-2, two clipped areas of region 190 designatedby numerals 196 and 198 are identified. Areas 196 and 198 are calculatedto be machined by a trochoidal-like tool path segment prior to themachining of the remainder of region 190 by a spiral tool path segment.

The remainder of region 190 does not include any islands, therefore aconverging spiral tool path segment is calculated to machine theremainder of region 190 with the internal boundary being a small circle191 of a radius which is generally smaller than the radius of the tool,and which is centered around the center of area of the remainder ofregion 190.

Subsequently, a spiral tool path segment for region 192 is calculated.As shown in FIGS. 1O-1 and 1O-2, one area of region 192, designated bynumeral 200 is identified by clipping. Area 200 is calculated to bemachined by a trochoidal-like tool path segment prior to the machiningof the remainder of region 192 by a spiral tool path segment.

Additionally, as shown in FIGS. 1P-1 and 1P-2, an additional area ofregion 192, designated by numeral 202 is identified by clipping.However, it is calculated that area 202 would be more efficientlymachined as a separate Type I region. Therefore, a separating channel210 which divides the remainder of region 192 into two Type I regionsdesignated by numerals 202 and 214 is calculated. Region 202 does notinclude any protrusions, therefore, as shown in FIGS. 1Q-1 and 1Q-2, aconverging spiral tool path segment is calculated to machine region 202with the internal boundary being a small circle 213 of a radius which isgenerally smaller than the radius of the tool, and which is centeredaround the center of area of region 202.

It is calculated that machining a separating channel 210 and machiningregion 202 as a Type I region results in a machining time which isshorter than the machining time of region 202 by a trochoidal-like toolpath segment.

Turning now to FIGS. 1R-1 and 1R-2, it is shown that region 214 includesone island 113 which is generally centrally located within region 214.Therefore, a converging spiral tool path segment 216 is calculated tomachine region 214 with the internal boundary being generally alongsidethe external perimeter of island 113. As shown in FIG. 1R-2, spiral toolpath segment 216, ultimately intersects with island 113 at intersectingpoint 218 at which point spiral tool path segment 216 is terminated. Itis appreciated that after machining segment 216, there may remain one ormore Type II regions adjacent to island 113 which are machined bytrochoidal-like tool path segments.

Turning now to FIGS. 1S-1 and 1S-2, it is shown that, the machining ofregion 156 is calculated. As shown in FIGS. 1S-1 and 1S-2, a clippedarea of region 156 designated by numeral 230 is identified by clipping.Area 230 is preferably calculated to be machined by a trochoidal-liketool path segment, and the remainder of region 156 is then calculated tobe machined by a spiral tool path segment.

It is appreciated that the calculation described hereinabove constitutesthe calculation of a tool path for the machining of a first step downwhich is a first phase in the machining of object 100. Throughout, theterm “step down” is used to describe a single machining phase at aconstant depth. As shown in FIG. 1C, the complete machining of object100 requires three step downs. Therefore, subsequent and similar to thecalculation described hereinabove, the tool path designer calculates themachining of second step down 119 and thereafter of third step down 120,thereby completing the entire rough machining of object 100. Preferably,the vertical distance between subsequent step downs is generally between1 and 4 times the diameter of the cutting tool.

It is appreciated that following the rough machining of a workpiece, anadditional stage of rest rough machining is calculated, which reducesthe large residual steps created by the series of step downs on thesloping surfaces of object 100.

Reference is now made to FIGS. 2A-2L-2, which illustrate the calculationof another tool path in accordance with a preferred embodiment of thepresent invention. FIGS. 2A and 2B are respective isometric and top viewillustrations of an object 400, which is another example of objects thatcan be fabricated in accordance with the present invention. Theconfiguration of the object 400 is selected to illustrate additionalvarious particular features of the present invention. It is noted thatany suitable three-dimensional object that can be machined by aconventional 3-axis machine tool may be fabricated in accordance with apreferred embodiment of the present invention.

As seen in FIGS. 2A & 2B, the object 400 is seen to have a generallyplanar base portion 402 from which one protrusion, here designated byreference numeral 404, extends. FIG. 2C shows stock material 410overlaid by a cross section 420 of object 400. Cross section 420 ischaracterized as having an external boundary 422 and an island 405corresponding to the cross section of protrusion 404 at the depth ofcross section 420.

In the illustrated example of FIG. 2C, cross section 420 is initiallyidentified as a Type III region 424 which includes one island 405. Asdescribed hereinabove, a plurality of nested offset contours iscalculated between the external boundary 422 of region 424 and aninnermost contour of region 424. The innermost contour is initiallycalculated to be overlapping with the external boundary of island 405.Therefore, as shown in FIGS. 2D-1 and 2D-2, a moat 428 is calculated tocircumvent island 405, and the innermost contour 430 is calculated to beimmediately external to the external boundary of moat 428.

As shown in FIGS. 2D-1 and 2D-2, innermost contour 430 and nestedinternal contour 440, external to innermost contour 430, define a TypeIII region 442. As shown in FIGS. 2E-1 and 2E-2, a diverging tool pathsegment 443 is initially calculated to spiral outwardly betweeninnermost contour 430 and nested internal contour 440, thereby creatingtwo residual regions 444 and 446. As shown in FIGS. 2F-1 and 2F-2,residual region 444 is calculated to be machined as a Type II region byemploying a trochoidal-like tool path segment. Similarly, as shown inFIGS. 2G-1 and 2G-2, residual region 446 is calculated to be machined asa Type II region by employing a trochoidal-like tool path segment.

Turning now to FIGS. 2H-1 and 2H-2, it is shown that a diverging spiraltool path segment is calculated to machine a Type III region 448 definedbetween nested internal contour 440 and nested internal contour 450.Subsequently, as shown in FIGS. 2I-1 and 2I-2, a diverging spiral toolpath segment is similarly calculated to machine a Type III region 452defined between nested internal contour 450 and nested internal contour460.

Turning now to FIGS. 2J-1 and 2J-2, it is shown that a diverging toolpath segment is calculated to machine a Type III region 468 definedbetween nested internal contour 460 and external boundary 422, therebycreating two residual regions 470 and 472. As shown in FIGS. 2K-1 and2K-2, residual region 470 is calculated to be machined as a Type IIregion by employing a trochoidal-like tool path segment. Similarly, asshown in FIGS. 2L-1 and 2L-2, residual region 472 is calculated to bemachined as a Type II region by employing a trochoidal-like tool pathsegment, thereby completing the calculation of the machining of object400.

It will be appreciated by persons skilled in the art that the presentinvention is not limited by what has been particularly shown anddescribed hereinabove. Rather, the invention also includes variouscombinations and subcombinations of the features described hereinaboveas well as modifications and variations thereof, which would occur topersons skilled in the art upon reading the foregoing and which are notin the prior art.

The invention claimed is:
 1. An object fabricated from a workpiecemachined using a computer controlled machine tool by directing arotating cutting tool along an asymmetric, non-circular spiral tool pathrelative to said workpiece, said asymmetric, non-circular spiral toolpath including a plurality of sequential loops, mutually separated bydifferent distances at different locations therealong, in each of whichan engagement angle between said rotating cutting tool and saidworkpiece gradually decreases from a maximum engagement angle to aminimum engagement angle and gradually increases from a minimumengagement angle to a maximum engagement angle, at least twice in asingle loop.
 2. An object fabricated from a workpiece machined using acomputer controlled machine tool by selecting a region of said workpieceto be removed by a rotating cutting tool and by directing said rotatingcutting tool along an asymmetric spiral tool path in said region of saidworkpiece, which spiral tool path maximizes the portion of said regionof said workpiece which is removed by said rotating cutting tool movingalong said asymmetric spiral tool path, and by directing said rotatingcutting tool along at least one trochoidal-like tool path in a remainingportion of said region of said workpiece which is removed by said toolmoving along said trochoidal-like tool path.
 3. An object fabricatedfrom a workpiece machined using a computer controlled machine tool by:selecting a region of said workpiece to be removed by a rotating cuttingtool; selecting a first portion of said region to be removed by anasymmetric spiral tool path, and by directing said rotating cutting toolalong at least one trochoidal-like tool path in said region of saidworkpiece; and wherein said selecting a first portion of said region isoperative to minimize the machining time necessary to remove saidregion.
 4. An object fabricated from a workpiece machined using acomputer controlled machine tool by: considering the cross section of adesired object to be fabricated from a workpiece; defining isolatedregions of said cross section on said workpiece surface which are not tobe removed as islands; initially directing said tool along a tool pathin a region not having islands; and upon said tool path encountering anisland, directing said tool along a tool path which defines a moatsurrounding said island.
 5. An object fabricated from a workpiecemachined using a computer controlled machine tool by: identifying atleast one open region for which a first machining time needed to removesaid region is longer than a second machining time needed to divide saidregion into two independent regions by removing a separating channel bya rotating cutting tool between said two independent regions andremoving said two independent regions; and defining in said region atleast one separating channel extending between two points on edges of anexternal boundary of said region, thereby dividing said region into atleast two independent regions.
 6. An object fabricated from a workpiecemachined using a computer controlled machine tool according to claim 5and wherein said object is fabricated also by directing said rotatingcutting tool along at least one trochoidal-like tool in said separatingchannel which is removed by said tool moving along said trochoidal-liketool path.
 7. An object fabricated from a workpiece machined using acomputer controlled machine tool by: identifying at least one semi-openregion for which a first machining time needed to remove said region byemploying a trochoidal-like tool path is longer than a second machiningtime needed to isolate said region by removing separating channelsbetween said region and all closed external boundary segments of saidregion and removing the remainder of said region; and by defining insaid region to be removed at least one separating channel between saidregion and all closed external boundary segments of said region, therebydefining a remaining open region to be removed.
 8. An object fabricatedfrom a workpiece machined using a computer controlled machine toolaccording to claim 7 and wherein said object is fabricated also bydirecting said rotating cutting tool along at least one trochoidal-liketool in said separating channel which is removed by said tool movingalong said trochoidal-like tool path.